With 10 minutes remaining at Stade Jean-Bouin and extra-time looking likely, Saint-Etienne came up trumps courtesy of Cros, who diverted Yohan Mollo's cross past goalkeeper Bobby Allain.
Saint-Etienne's match-winner came after an entertaining half that saw both teams level at the break.
The Ligue 1 giants hit the front through Ricky van Wolfswinkel in the 18th minute and they were further boosted when Julien Ielsch was shown a straight red card seven minutes later.
However, third-tier outfit Red Star managed to restore parity in the 28th minute after former Watford and Fulham winger Hameur Bouazza found the back of the net from close range.
Despite their numerical disadvantage, Red Star continued to thwart Saint-Etienne in the second half but they were eventually breached in the 80th minute, a moment that proved decisive.
Auxerre and Concarneau required penalties to progress to the round of 16 on Tuesday.
Jean-Luc Vannuchi's Auxerre defeated hosts Le Poire-sur-Vie 6-5 on penalties after scores were level 1-1 at the end of 120 minutes.
Concarneau were 4-1 winners in a shoot-out at Iris Club de Croix following a goalless stalemate.
Meanwhile, Henry Gbizie and Georges Gope-Fenepej were on target as Boulogne defeated Quevilly 2-0.
